The Cops

The Cops appear in most games in the Carmageddon series, although they take various different forms. They lie in wait on many levels, but will wake up, turn on their sirens and come after the player if they see him/her doing something illegal. Considering competitors generally race around at high speed, smacking into other cars and running through zombie/human crowds with impunity, this could be often.
These cops don't just pull the player over and write a ticket though - they try to batter him/her to death!

The police vehicle is an opponent, rather than a police vehicle. It can be bought like a regular car.

12 cop cars have to be defeated in Carmageddon II mission The Bruise Brothers.

The Copcar is an obvious homage to The Blues Brothers' Bluesmobile. The description is taken verbatim from Elwood Blues (Dan Akroyd)'s description of the Bluesmobile in the movie.

Thirteen vehicles were used as Bluesmobiles in total for The Blues Brothers, most of which were destroyed during filming. Almost 60 police cars were also destroyed - the film held the world record for the most cars destroyed in one film, until it was surpassed by its own sequel.

The default Cop Car in TDR 2000 is driven by the only female police officer in the series.

The same vehicle can also show up as an opponent. If defeated as one, it can be bought.

Unused driver descriptions in TDR2000 name the (female) CopCar driver as Harry Killahan. Along with the quote, it's an obvious reference to rogue lawman Harry Callahan from Dirty Harry.

The front doors of the Pigs' vehicle (the 1920s "paddywagon" police car) bear an emblem with the words "The 3 Pigs". This is a reference to the fairy tale Three Little Pigs.

"Pig" is a derogatory term for a Police officer.

In the original Carmageddon, the Squad Car is the only vehicle which can not be visually damaged - the bodywork trashed powerup doesn't bend the bodywork.

In Funsize, the bodywork trashed pickup does affect the vehicle. Since Cops and Opponents can be affected by powerups, this can occur to Squad Cars when not driven by the player. Normal damage still doesn't deform the vehicle.

In Carmageddon, the Squad Car is not normally allowed to be an opponent or driven by the player (unlike the Suppressor, it's not stealworthy) which is why there is no sprite for the Squad Car in the Select grid position menu and instead a Red Eagle as a placeholder.